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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/vector_fe/vector_fe_ex4" target="_blank">Open vector_fe_ex4 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example vector_fe_ex4:
*   ./example-opt element_type=TET10 -pc_type jacobi
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=3
  n_nodes()=2585
    n_local_nodes()=2585
  n_elem()=1536
    n_local_elem()=1536
    n_active_elem()=1536
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=2156
    n_local_dofs()=2156
    max(n_local_dofs())=2156
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=2156
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.3581
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 25
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 5.02926
Linear solve starting, tolerance 1e-12
Linear solve finished, step 29, residual 1.88386e-13
Trying full Newton step
  Current Residual: 1.14961e-05
  Nonlinear step: |du|/|u| = 1, |du| = 8.59662
Assembling the System
Nonlinear Residual: 1.14961e-05
Linear solve starting, tolerance 1e-12
Linear solve finished, step 355, residual 1.83282e-25
Trying full Newton step
  Current Residual: 1.01399e-14
  Nonlinear solver converged, step 1, residual reduction 2.01619e-15 < 1e-06
  Nonlinear solver converged, step 1, relative step size 2.12393e-12 < 1e-06
L2-Error is: 0.421384
HCurl semi-norm error is: 1.00529
HCurl-Error is: 1.09003

***************************************************************
* Done Running Example vector_fe_ex4:
*   ./example-opt element_type=TET10 -pc_type jacobi
***************************************************************
***************************************************************
* Running Example vector_fe_ex4:
*   ./example-opt element_type=HEX20 -pc_type jacobi
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=3
  n_nodes()=425
    n_local_nodes()=425
  n_elem()=64
    n_local_elem()=64
    n_active_elem()=64
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=300
    n_local_dofs()=300
    max(n_local_dofs())=300
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=300
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 23.4
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 33
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 10.5823
Linear solve starting, tolerance 1e-12
Linear solve finished, step 8, residual 1.77336e-12
Trying full Newton step
  Current Residual: 0.00343467
  Nonlinear step: |du|/|u| = 1, |du| = 3.91397
Assembling the System
Nonlinear Residual: 0.00343467
Linear solve starting, tolerance 1e-12
Linear solve finished, step 65, residual 8.76357e-25
Trying full Newton step
  Current Residual: 3.98932e-15
  Nonlinear solver converged, step 1, residual reduction 3.76978e-16 < 1e-06
  Nonlinear solver converged, step 1, relative step size 6.67301e-12 < 1e-06
L2-Error is: 0.172154
HCurl semi-norm error is: 1.47497
HCurl-Error is: 1.48498

***************************************************************
* Done Running Example vector_fe_ex4:
*   ./example-opt element_type=HEX20 -pc_type jacobi
***************************************************************
***************************************************************
* Running Example vector_fe_ex4:
*   ./example-opt element_type=HEX27 -pc_type jacobi
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=3
  n_nodes()=729
    n_local_nodes()=729
  n_elem()=64
    n_local_elem()=64
    n_active_elem()=64
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=300
    n_local_dofs()=300
    max(n_local_dofs())=300
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=300
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 23.4
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 33
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 10.5823
Linear solve starting, tolerance 1e-12
Linear solve finished, step 8, residual 1.77359e-12
Trying full Newton step
  Current Residual: 0.00343547
  Nonlinear step: |du|/|u| = 1, |du| = 3.91397
Assembling the System
Nonlinear Residual: 0.00343547
Linear solve starting, tolerance 1e-12
Linear solve finished, step 56, residual 1.14044e-24
Trying full Newton step
  Current Residual: 5.16952e-15
  Nonlinear solver converged, step 1, residual reduction 4.88504e-16 < 1e-06
  Nonlinear solver converged, step 1, relative step size 6.67363e-12 < 1e-06
L2-Error is: 0.172154
HCurl semi-norm error is: 1.47497
HCurl-Error is: 1.48498

***************************************************************
* Done Running Example vector_fe_ex4:
*   ./example-opt element_type=HEX27 -pc_type jacobi
***************************************************************
</pre>
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